Simplify the following expression: $a = \dfrac{-44q}{11q + 22}$ You can assume $q \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-44q = - (2\cdot2\cdot11 \cdot q)$ The denominator can be factored: $11q + 22 = (11 \cdot q) + (2\cdot11)$ The greatest common factor of all the terms is $11$ Factoring out $11$ gives us: $a = \dfrac{(11)(-4q)}{(11)(q + 2)}$ Dividing both the numerator and denominator by $11$ gives: $a = \dfrac{-4q}{q + 2}$